Math Courses Research Articles

Breaking the mold: Study strategies of students who improve their achievement on introductory biology exams.

Students' use of learning strategies (i.e., what students do when studying) is linked to their achievement in undergraduate science, technology, engineering, and math (STEM) courses, and several study strategies have been individually associated with course and exam grades in multiple contexts. In this study, we surveyed students in a learner-centered, large-enrollment introductory biology course about their study strategies. We aimed to identify groups of strategies that students often reported together, possibly reflecting broader approaches to studying. Exploratory factor analysis revealed three groups of study strategies frequently co-reported (which we named housekeeping strategies, use of course materials, and metacognitive strategies). These strategy groups map onto a model of learning that associates specific suites of strategies to phases of learning, which correspond to different levels of cognitive and metacognitive engagement. Consistent with previous work, only some study strategies were significantly associated with exam scores: students reporting higher use of course materials and of metacognitive strategies earned higher scores on the first course exam. Students who improved on the subsequent course exam reported increasing their use of housekeeping strategies and of course materials. Our findings contribute to a deeper understanding of students' approaches to studying in introductory college biology and of the relationships between study strategies and achievement. This work may support instructors in adopting intentional classroom practices to foster students' development as self-regulated learners, able to identify expectations and criteria for success and to implement appropriate and effective study strategies.

The application of discovery learning as an effort to improve mathematical problem solving skills

Research conducted is a type of experimental research that has the following objectives: (1) to know the correlation between the learning achievement of students who use the discovery learning method and the conventional method in the applied math course , (2) to know the level of effectiveness of student outcomes using conventional and discovery learning methods, (3) to know the level of effectiveness of student of learning results by using the discovery learning method and conventional methods. The research conducted has a population of D3 Mechanical Engineering study program students in Semester 2 Academic Year 2022/2023 Harapan Bersama PolytechnicSamples taken using grade 2A and 2C randomly where the two gradees with the division of grade 2A is the experiment grade and grade 2C is the control grade. The series of processes in the research method consists of preliminary tests, namely validity, reliability, difficulty level, and question differentiation. After being given the learning treatment, then analyzed by statistical tests. The results of the analysis provide an overview the results that in an experimental grade with an average result of 78 and a control grade with average results. Result of 62, then a statistical test is obtained sedangkan from the analysis results, it can be concluded that students who get treatment with the discovery learning method get better learning outcomes than the class that does not. do not get discovery learning treatment.

Reimagining Community College Math Reform Amid COVID-19

Objective: In Spring 2020 when COVID-19 hit, community colleges moved almost all classes online. This disruption impacts recent math reforms, including contextualization, raising concerns about sustained faculty and institutional leadership commitment. This study investigated how community college faculty teaching contextualized math courses adapted their instruction in response to COVID-19-related disruptions and how community college and instructional leadership addressed math contextualization efforts in response to COVID-19. Methods: Using multiple case studies, we conducted interviews with faculty and institutional leaders from two large community colleges in a Midwestern state. We also integrated field notes, observations, lesson plans, project documentation, and other contextual information as complementary data. Results: Three themes revealed how faculty and institutional leaders navigated the process of adapting contextualization efforts throughout the pandemic: reaching out to create community remotely, reimagining contextualization or pushing the pause button, and skilling up to persist through and toward change. Contribution: This study provides insight into the unique challenges and innovations due to sudden yet enduring disruptions that impact instruction, faculty development, and institutional support around instructional reform in the community college. This research informs faculty and institutional leaders navigating sustained efforts around math reform to identify actions to help institutions and their faculty continue advancing high-impact approaches and initiatives to math instruction in any environment.

Course-level factors and undergraduate engineering students’ ratings of instruction

ABSTRACT Post-course instructor ratings are a common practice at universities in Europe, Australia, and North America. Rather than solely describing teaching practice, however, such ratings may be associated with a range of non-pedagogical factors. We explored engineering students’ instructor ratings at a large United States institution, investigating relationships between overall instructor rating and some of those non-pedagogical factors, including subject area, class size, and students’ course grades. Instructor ratings were more favourable in humanities courses than in science or math courses, and students gave higher ratings to instructors who taught smaller class sizes. The strongest relationship existed between overall rating and students’ course grades: students who received A’s rated instructors an average 0.84 points higher on a 6-point scale than students who received F’s. Students who withdrew from a course provided the lowest instructor ratings. When instructor ratings are used as metrics of teaching ability in discussions related to promotion, tenure, or salary adjustments, there is an inherent inequity in the system that must be acknowledged beyond already well-documented biases, as non-pedagogical factors often outside of the instructor’s control may be significantly associated with those ratings.

Prospective Teachers’ Perceptions, Reliance, and Barriers to ICT Integration in Mathematics Learning

Prospective teachers’ (PTs’) ICT integration (ICTi) for learning math (LM) has been studied in the global context, however, it lacks in the local context. This study served to bridge the gap by exploring PTs’: perceptions toward ICT competence and integration; reasons for relying on technology; and the challenges encountered while LM. The methodology was grounded in interpretivism, induction, mono-method-qualitative, case study, and cross-sectional components. The participants’ selection was based on convenient and purposive techniques. Data were collected through semi-structured interviews (SSI) and focus group discussions (FGD) and were analyzed using thematic data analysis. The findings informed positive perceptions of PTs toward ICTi where the purpose of relying on technology varied across participants. Though ICTi was found important, still there are inherent challenges associated with its integration, for example, scanning online material, encoding math language, and limited awareness of mathematics application software. The recommendations necessitate the development of special programs to offer hands-on learning experiences along with mitigating challenges for the prospective teachers to integrate ICT for LM. Future researchers may focus on variables through the blended model of teaching and learning that impact the academic performance of students in a math course.

Primary School Teachers’ Attitudes and Views toward STEM Education

To produce ideas, products, and industries for the 21st-century scientists, technologists, engineers, and mathematicians are needed. It is necessary to increase the number of people who provide technical support to the problems of individuals, set a standard for the lives of the people of the world, and manage global or national life with a sustainable decision-making mechanism. Raising these individuals can only be possible through education. Countries trying to make themselves technologically aware are looking for modern methods of teaching, one of which is science, technology, engineering, and mathematics (STEM) education. This research aimed to determine the attitude of primary school teachers toward the STEM approach and to find out their views on the STEM approach in the primary school curriculum. Students encounter the STEM approach while they are in primary school. However, all primary school teachers do not teach only science and math; they also teach other courses such as social sciences, language, ethics, music, and art. Therefore, teacher orientation toward the STEM approach in science and math courses is crucial. This research was concurrent mixed-method research that collected quantitative and qualitative data simultaneously. The STEM attitude scale was used as a quantitative data collection tool and qualitative data were collected using semi-structured interviews and focus group interviews. The qualitative data were analyzed using descriptive and content analyses. The study’s most important results showed no significant difference between STEM attitude scores regarding technology familiarity. Another significant result was that teachers who participated in quantitative and qualitative studies scored above average on the STEM attitude scale. The research results imply that pre-service primary school teachers should be given the STEM approach.

The Where and Why of Accelerated Middle-School Mathematics

Students in any grade level vary widely in their mathematics achievement, with the typical classroom including four to seven grade levels of mathematics proficiency. Due to this large range of mathematics learning needs, some schools offer certain courses in earlier grades than is typical. In this study, we analyzed multiple, large, national datasets to understand which schools provide access to seventh-grade algebra and eighth-grade geometry. Next, we explored what factors predicted school-level access to those courses and the proportion of eligible students enrolled in either course. We found that access varies widely across, and even within, states and districts, with factors such as parental education and within-district economic segregation remaining predictive even after controlling for average school achievement. In general, predictors of the proportion of a school identified as gifted were weaker, but schools in more-segregated districts and those with larger proportions of White students enrolled did tend to enroll fewer students in either math course.

Syllabus 2.0: Using Videos to Make the Syllabus Active

Given the wealth of research available on what components to include in a syllabus and how that affects instructor perception, there is a lack of research on how to present the syllabus to engage students in learning about the course. Our study examined the implementation of two multimedia syllabi developed for large lecture math courses: a graphic syllabus and a video version. After reviewing their respective syllabi, students were given a syllabus content quiz and course perception survey. Findings indicate no significant difference between students’ syllabus quiz performance and overall survey responses between groups. Students responded favorably to the survey regardless of syllabus type. Last, there was no observed relationship between the length of each syllabus segment video and the frequency at which students watched each segment. Implications of this study will address engagement with the syllabus and provide additional considerations for syllabus development.

Does question order matter on online math assessments? A big data analysis of undergraduate mathematics final exams

AbstractBackgroundThe sudden growth in online instruction due to COVID‐19 restrictions has given renewed urgency to questions about remote learning that have remained unresolved. Web‐based assessment software provides instructors an array of options for varying testing parameters, but the pedagogical impacts of some of these variations has yet to be examined.ObjectivesThe current study examines whether question order affects student performance on online college math assessments. Drawing on the literature of testing and math anxiety, we hypothesized that difficult questions near the beginning of an assessment would have a destructive effect on student confidence, which would in turn have a deleterious effect on their performance.MethodsWe employed an observational ‘big data’ methodology, analysing 23,468 final exams completed by students in 10 different courses over eight semesters at a Math Emporium in a large technical university in the eastern United States. Students were freshmen and sophomores enrolled in non‐engineering math courses. We regressed the final score on the difficulty level of the first and second questions, controlling for several other factors.Results and ConclusionsWe found that several factors—day of the week, amount of time before the deadline, number of minutes spent on the exam—have more of an impact on score than question order. This pattern was consistent across sexes.TakeawaysOur findings contradict some previous studies, which have found that difficult early questions degrade student performance, and that this affect is more pronounced in females. This work enriches our understanding of how students respond to online assessment.

Students’ perceptions in undergraduate online math courses

The purpose of this qualitative study was to understand how undergraduate math students perceive their learning in an online learning environment. A review of the literature revealed a need for additional qualitative research on the perceptions of students in the online learning environment. The specific elements of interest were technology, communication, and assessment. The study used a qualitative descriptive case study design. Purposive sampling was used to sample six online undergraduate math students. Online questionnaires and follow-up interviews provided data for analysis. Interpretive analysis highlighted emergent themes to form a true representation of students’ perceptions. The results revealed that students perceived technology as a supportive tool that could not replace the need for teacher–student interaction and engagement. In addition, online students perceived communication as an essential classroom element. Participants considered online assessment measures ineffective without useful feedback. Educational stakeholders could use the study’s findings to make informed instructional design decisions that could increase student success rates in undergraduate online math courses. Also, researchers might use the study findings to identify instructional elements that could potentially lead to increased learning gains.

Self-Placement in Math Courses at U.S. Community Colleges: Contributing Factors and Impacts on Student Success

Self-placement in math is becoming increasingly popular in community colleges in the U.S., where students will decide for themselves whether to enroll in non-credit developmental (or remedial) math courses. To fully understand the factors associated with students’ math enrollment choices and the long-term effects of initial math enrollment choices, we use data from all first-time-in-college students in the Florida College System to conduct a multinomial logistic regression analysis and an inverse-probability regression adjustment analysis. We find that most students chose to directly enroll in college-level math, with significant differences by gender and high school math preparation. First-year math enrollment choices were significantly associated with likelihood of passing college-level math and the number of college credits by the third year.

An astonishing regularity in student learning rate.

Leveraging a scientific infrastructure for exploring how students learn, we have developed cognitive and statistical models of skill acquisition and used them to understand fundamental similarities and differences across learners. Our primary question was why do some students learn faster than others? Or, do they? We model data from student performance on groups of tasks that assess the same skill component and that provide follow-up instruction on student errors. Our models estimate, for both students and skills, initial correctness and learning rate, that is, the increase in correctness after each practice opportunity. We applied our models to 1.3 million observations across 27 datasets of student interactions with online practice systems in the context of elementary to college courses in math, science, and language. Despite the availability of up-front verbal instruction, like lectures and readings, students demonstrate modest initial prepractice performance, at about 65% accuracy. Despite being in the same course, students' initial performance varies substantially from about 55% correct for those in the lower half to 75% for those in the upper half. In contrast, and much to our surprise, we found students to be astonishingly similar in estimated learning rate, typically increasing by about 0.1 log odds or 2.5% in accuracy per opportunity. These findings pose a challenge for theories of learning to explain the odd combination of large variation in student initial performance and striking regularity in student learning rate.

Investigating algorithm-oriented flexibility and structure-informed flexibility in mathematics learning

Procedural flexibility is a crucial element of deep procedural knowledge involving the selection of “the most appropriate strategy.” However, there exists unavoidable nuance when one attempts to define “the most appropriate” strategy, which leads to two types of procedural flexibility: (a) structure-informed flexibility (Struct-Flex), which refers to a preference for situationally appropriate strategies; (b) algorithm-oriented flexibility (Algo-Flex), which refers to a preference for standard algorithms. The current study investigated the distinction between these two flexibility types and tested potential predictors for both types of flexibility. The study data were collected from 412 Grade 9 through 12 students from 19 math classrooms in the southeastern region of the U.S. Chi-squared tests and regression models revealed that: (a) problem type was strongly correlated to and predictive of a preference for using algorithms in algebra; (b) students’ current high school math course grade was associated with preference for standard algorithms; (c) students’ current high school math course level and their classroom assignment were related to preference for situationally appropriate strategies. The results suggest that, in this sample, Algo-Flex was as prevalent as Struct-Flex, and the two flexibility types had different predictors. This paper can advance our practical knowledge of U.S. students’ strategy choices. The identified predictors of Algo-Flex and Struct-Flex can also inform the design of relevant educational interventions. Future studies may explore longitudinal datasets to untangle the relationship between course level, age, and flexibility, as well as examine flexibility in Asia in comparison to Europe and North America.

Searching for short-term motivational alignment and spillover effects: A random intercept cross-lagged analysis of students’ expectancies and task values in math-intensive study programs

Students’ expectancy and value beliefs about math influence their academic choices and success in math-intensive study programs. Short-term declines in these motivational beliefs can serve as early warning signs of academic difficulties and dropout. However, such short-term motivational changes are underresearcherd. Based on Eccles et al.’s (2020) situated expectancy-value theory, this study analyzed within-person changes in the associations among students’ course-specific (summative) or week-specific (situated) expectancies and task values in gateway math courses for students in physics, math, or math teacher education majors (N = 773). Random intercept cross-lagged panel models showed increasing within-person alignment between students’ course-specific expected success and intrinsic/utility values (but not costs) over one semester. This alignment was linked to unidirectional spillover (i.e., cross-lagged) effects from expectancy to intrinsic/utility values. Students’ week-specific expectancy-value beliefs, reported at the beginning of the semester, showed no significant alignment and spillover effects. Differences in students’ course- or week-specific expectancy-value beliefs favored male and higher-achieving students and were largely time-invariant. Alignment between course-specific expectancy and value beliefs was higher for students who failed or dropped out of their math courses compared to those who succeeded. Greater motivational alignment can thus indicate greater disengagement from (math) coursework in challenging academic contexts. These findings highlight the importance of differentiating between-person and within-person motivational processes, suggest that summative versus situation-specific assessments of motivational beliefs may show different developmental patterns, and demonstrate that motivational alignment and spillover effects can be a sign of maladaptive motivational processes concerning students’ persistence in challenging STEM contexts.

Gender Differences in Class-related Emotional Experiences: A Study of Mathematics Course

In education, students experience different emotions, which affect their academic performance, engagement, and achievement. In the classroom, these emotional experiences of students are called academic emotions (Lei & Cui, 2016). This paper holds two-fold aims: to inquire about class-related emotions; and to find gender differences in the emotional experiences of undergraduates of a math course. The theoretical framework was grounded in control value theory. The purpose of the study was achieved by adopting a positivist paradigm, and applying a quantitative research method. The achievement emotions questionnaire (2000) was adapted as a data collection tool for class-related emotions. The data were collected from 162 undergraduates. The descriptive analysis was run for comparing group means on SPSS v. 23. The findings reported more positive emotional experiences: pride and enjoyment, and less negative emotional experiences: anxiety, anger, hopelessness, shame, and boredom in learning math in students. Moreover, interesting differences were found in class-related emotions between males and females. Future researchers direct focus on assessing test-related, learning-related, and teacher-related emotions of students learning science courses, and uncover underlying factors of negative emotions and environmental inciters of emotions from an interpretivist's perspective.

A Comparative Study of High School Students' Math Achievement and Attitudes: Do Math Teacher Qualifications Matter?

Using nationally representative High School Longitudinal Study of 2009 data, this quantitative study examined how math teacher qualifications affect U. S. 9th graders’ math achievement and attitudes. The study is guided by the Cognitive Apprenticeship Theory that emphasizes that expert teachers enable students to learn as apprentices and construct knowledge within the activity, context, and culture in which it is learned. The study shows that not only does cognitive apprenticeship enable skill development and knowledge acquisition, but it shapes student math self-efficacy and interest in the subject, and it develops their math identity if students viewed math teachers as role models. The study employs a comparative research design to explore the main effects and interaction between teachers’ credential type and field of study degree on student outcomes. One notable finding is that teacher credentials (i.e., level of education certification) affected student math achievement and math identity but had weaker effects on math self-efficacy, math utility and interest in math courses. Second, holding a math degree affected students’ math achievement and math identity, while holding a degree in education had some positive effects on increasing students’ interest in math courses. Results have direct implications for the field of Mathematics Education showing that teacher qualifications affect student beliefs and attitudes toward mathematics.

Relative importance of students' expectancy-value beliefs as predictors of academic success in gateway math courses.

Math-intensive fields in postsecondary education, such as physics and math, often struggle with high student dropout rates. Motivational declines after the transition to postsecondary education are a key factor underlying students' achievement difficulties and decisions to leave these fields. A better understanding of which motivational factors play a particularly central role in predicting achievement difficulties and dropout decisions is needed to inform potential interventions. Thus, drawing on Eccles' expectancy-value theory, we examined changes in the relative importance of students' expected success and different task values as unique or joint predictors of students' academic success and course dropout across three time points within a semester. Data were collected in gatekeeper math courses for physics and math majors (N = 811). Commonality analyses showed an increasing overlap in the predictive effects of students' expectancies and values on later academic outcomes, which indicates convergence in these motivational beliefs, as they likely influence each other over time. A significant shift in the relative importance of students' expectancies and values occurred after the transition to postsecondary education, highlighting a sensitive time point for interventions. Pre-existing achievement, socioeconomic, and gender differences lost some of their unique predictive power toward the midpoint of the semester.

U.S. Ninth Graders' Math Course Placement at the Intersection of Learning Disability Status, Race, and Socioeconomic Status.

This study integrates an intersectional framework with data on 15,000 U.S. ninth graders from the High School Longitudinal Study of 2009 to investigate differences in ninth-grade math course placement at the intersection of adolescents' learning disability status, race, and socioeconomic status (SES). Descriptive results support an increased liability perspective, with the negative relationship between a learning disability and math course placement larger for adolescents more privileged in terms of their race and/or SES. Adjusted results suggest that the lower math course placements of youth with learning disabilities are due to cumulative disadvantage rather than disability-related inequities in the transition to high school for youth of diverse racial and socioeconomic backgrounds. In addition to demonstrating the importance of intersectional perspectives, this study provides a roadmap for future studies by introducing the new perspective of increased liability to be used in conjunction with the widely employed perspective of multiple marginalization.

High school transcript placement in developmental mathematics courses: A case study at one college

Historically, college students who require remediation in mathematics have been placed into developmental mathematics courses. Accurate placement is important for student success; inaccurate placement in a low-level course could lengthen a students’ time to degree completion. Placement policies have tended to focus on a high-stakes placement test, but more holistic approaches have been recommended. This study investigated success outcomes for students placed with a holistic approach of evaluating high school transcripts. Students who were placed into one of three developmental mathematics by their high school transcript at a suburban community college in North-eastern United States were selected for this study. A non-experimental, retrospective research study was conducted. Archival data of students who took a developmental mathematics course from fall 2015 through spring 2019 and had a high school transcript on file were chosen for this study. Findings from chi-square analyses indicated that high school transcripts that consider mathematics course grades are a viable placement option for developmental math courses, particularly the two lower-levels. However, lower than desired success rates suggest that placement is only the first step to increasing student achievement. A lack of high school transcripts suggests some students would prefer to take a placement test, particularly for students in the upper-level course on a college algebra path. A challenge for community college advisors will be creating an equitable placement policy for students who do not have a recent high school transcript.

The Impact of Taking Math Courses on Nursing Students’ Skills to Calculate Drug Dosages: A Comparative Study

The Impact of Taking Math Courses on Nursing Students’ Skills to Calculate Drug Dosages: A Comparative Study